Problem: A group of adults and kids went to see a movie. Tickets cost $$8.00$ each for adults and $$2.50$ each for kids, and the group paid $$31.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Explanation: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8x+2.5y = 31}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${8}{(y-4)}{+ 2.5y = 31}$ Simplify and solve for $y$ $ 8y-32 + 2.5y = 31 $ $ 10.5y-32 = 31 $ $ 10.5y = 63 $ $ y = \dfrac{63}{10.5} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(6)}{ - 4}$ ${x = 2}$ You can also plug ${y = 6}$ into ${8x+2.5y = 31}$ and get the same answer for $x$ ${8x + 2.5}{(6)}{= 31}$ ${x = 2}$ There were $2$ adults and $6$ kids.